A recognized method for cooling and lubricating gas turbine engine bearings and seal runners includes the steps of spraying oil onto an inside surface of a rotating shaft and conducting the oil to the bearings and seal runners through orifices in the shaft. Forces on the oil resulting from shaft rotation adhere the oil to the shaft as a thin film on the inside surface and motivate the oil through the orifices to the seal runners and the bearings. In practicing this method, several systems have been proposed for metering or distributing the oil between the bearings and seal runners. In one system, the orifices meter the flow. In another system, different sized pockets are formed on the inside surface of the rotating shaft to capture oil in proportion to their areas exposed to the oil spray. In the first mentioned system, the orifices may be so small as to be susceptible to clogging by debris in the oil. In the second mentioned system, difficult machining operations may be required if the pockets are formed directly on the shaft or a weight penalty may be experienced if the pockets are formed on a metal insert installed on the inside surface of the shaft. In the latter arrangement, seal rings between the shaft and the insert are additional parts required to practice the method. A metering system according to this invention implements the aforesaid cooling and lubricating method with a flexible, resilient insert which cooperates with the shaft in defining the oil pockets but which is lighter than prior metal inserts and requires no retention elements and no seal rings.